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Friday, July 10, 2015

Lychrel Numbers

A Lychrel number is an integer (any length) that does NOT eventually form a palindromic number (reading the same backwards & forwards) after following a process of reversing its digits and adding, reversing and adding, etc....
for example, starting with 837:

837          1575        7326        13563         50094
738          5751        6237        36531         49005
1575        7326      13563        50094         99099      <== palindromic

Simple enough, and in most cases a palindrome is arrived at within fairly short order.
BUT in the case of 196 no such palindrome has ever been reached. There is no proof that one does not exist somewhere waaaaay out there, though it seems unlikely; but why? why 196? There are actually several additional numbers thus far not found to produce palindromes, 196 is just the smallest of them. In fact, NO Lychrel numbers have ever been proven to exist in base 10, just plenty of candidates.

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1 comment:

Chris G said...

Everybody says 196 is the smallest Lychrel. I suggest the smallest is 097 since the reverse is 790. Sum the two and you get 788. This is also a Lychrel and on the same path as 196 since 196+691=887, reverse:788.